This is a treatise on modern probability theory. In the first few chapters, Jaynes quite succinctly derives the theory as what would seem at first blush like a mild extension of binary logic. The whole thing is a bit of a tome but the chapters are not ordered in a strict logical manner, so you can skip around after the first derivation part.
The whole book is gold, though. In my experience, a lot of texts are organized as "statistical toolbags" whereas Jaynes hammers in the point that there are solid principles underlying the theory that, when kept clearly in mind, quickly empower you to approach even tricky problems.
There is even an entire chapter devoted to dispelling "probability paradoxes" which arise from the (mis)use of infinite sets. Jaynes clears these up neatly, making a strong case for always using clearly-defined limiting processes when dealing with non-finite systems.
The foundations presented in this book do stand in opposition to the standard approach using Kolmogorov Axioms. Jaynes' approach is inherently finitistic, which IMHO, makes the reasoning a whole lot more obvious.
You can find in PDF by typing it into your favorite search engine.
Taylor and Karlin, "An Introduction to Stochastic Modeling"